Motivated by the so-called shortfall risk minimization problem,we consider Merton-s portfolio optimization problem in a non-Markovianmarket driven by a Lévy process, with a bounded state-dependent utilityfunction. Following the usual dual variational approach, we show that thedomain of the dual problem enjoys an explicit -parametrization,- built ona multiplicative optional decomposition for nonnegative supermartingalesdue to Föllmer and Kramkov 1997. As a key step we prove a closure propertyfor integrals with respect to a fixed Poisson random measure, extending aresult by Mémin 1980. In the case where either the Lévy measure of has finite number of atoms or for a process and adeterministic function , we characterize explicitly the admissible tradingstrategies and show that the dual solution is a risk-neutral local martingale.